Paper Citation Record · LEDGER

Zeroth-Order Optimization at the Edge of Stability

As of 22 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 0 inbound Pith citation observations for arXiv:2604.14669.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2604.14669 v2

Coverage vector

measured 16 of 16 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-12T20:06:39.488359Z

measured 16 of 16 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

16 of 16 outbound references displayed

verified exact0
verified fuzzy0
unresolved15
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b35f47f4-3dbb-4060-b3d5-98aa26a2e7f5 · outbound

This paper cites and Beneventano, P.

Zeroth-Order Optimization at the Edge of Stability and Beneventano, P

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-12T20:06:39.488359Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d0e68863-1604-4d88-83dc-82d93675190c · outbound

This paper cites Adaptive Gradient Methods at the Edge of Stability.

Zeroth-Order Optimization at the Edge of Stability Adaptive Gradient Methods at the Edge of Stability

Reference 2

Resolution: unresolved; no resolver link, observed 2026-07-12T20:06:39.488359Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f1f63203-12e3-4bab-a3b4-d460b16298df · outbound

This paper cites The large learning rate phase of deep learning: the catapult mechanism.

Zeroth-Order Optimization at the Edge of Stability The large learning rate phase of deep learning: the catapult mechanism

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-12T20:06:39.488359Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 43e7bd24-af27-4f3e-b1f2-ea19c91a445e · outbound

This paper cites Evolution Strategies as a Scalable Alternative to Reinforcement Learning.

Zeroth-Order Optimization at the Edge of Stability Evolution Strategies as a Scalable Alternative to Reinforcement Learning

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-12T20:06:39.488359Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 998d4258-d338-4cbd-90e9-4c2efe2e99d3 · outbound

This paper cites Type-II Saddles and Probabilistic Stability of Stochastic Gradient Descent.

Zeroth-Order Optimization at the Edge of Stability Type-II Saddles and Probabilistic Stability of Stochastic Gradient Descent

Reference 5

Resolution: unresolved; no resolver link, observed 2026-07-12T20:06:39.488359Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c3e76b39-ff5e-4480-a047-088e9c33344e · outbound

This paper cites Applyings Σp¨qand cancellings ‹ ą0gives r“˜η 2 sΣ ˆ´ Id´ 1 r M ¯´1 sQΣ ˙.

Zeroth-Order Optimization at the Edge of Stability Applyings Σp¨qand cancellings ‹ ą0gives r“˜η 2 sΣ ˆ´ Id´ 1 r M ¯´1 sQΣ ˙

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-12T20:06:39.488359Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 44ff55a6-394e-4f20-a36d-9d40b2fd0da1 · outbound

This paper cites Experimental details In this section, we provide additional experimental details.

Zeroth-Order Optimization at the Edge of Stability Experimental details In this section, we provide additional experimental details

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-12T20:06:39.488359Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4fd9d2fa-81ca-4f40-bfe9-72a7ce2ae591 · outbound

This paper cites • Vision Transformer (ViT).A Vision Transformer (Dosovitskiy et al.,.

Zeroth-Order Optimization at the Edge of Stability • Vision Transformer (ViT).A Vision Transformer (Dosovitskiy et al.,

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-12T20:06:39.488359Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4cc3cd92-b3de-414c-a279-0329e5338190 · outbound

This paper cites Top eigenvalue and trace estimation.During training, we log curvature statistics every 1,000 iterations.

Zeroth-Order Optimization at the Edge of Stability Top eigenvalue and trace estimation.During training, we log curvature statistics every 1,000 iterations

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-12T20:06:39.488359Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fc53c5ee-ec81-4fbf-892d-78048d134d71 · outbound

This paper cites an unresolved cited work.

Zeroth-Order Optimization at the Edge of Stability Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-12T20:06:39.488359Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5a50d29c-f8f3-4617-b4ff-a87bb9677217 · outbound

This paper cites an unresolved cited work.

Zeroth-Order Optimization at the Edge of Stability Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-07-12T20:06:39.488359Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 76b2ce5c-0166-4dad-861d-b348dbadee82 · outbound

This paper cites (2025, Appendix B.3), we train full-batch ZO-GD, ZO-GDM, and ZO-Adam and track the corresponding mean-square stability quantities.

Zeroth-Order Optimization at the Edge of Stability (2025, Appendix B.3), we train full-batch ZO-GD, ZO-GDM, and ZO-Adam and track the corresponding mean-square stability quantities

Reference 12

Resolution: unresolved; no resolver link, observed 2026-07-12T20:06:39.488359Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d326d28a-6f68-4178-8a53-bf789c945589 · outbound

This paper cites (2025, Appendix B.3), we train full-batch ZO-GD, ZO-GDM, and ZO-Adam and track the corresponding mean-square stability quantities.

Zeroth-Order Optimization at the Edge of Stability (2025, Appendix B.3), we train full-batch ZO-GD, ZO-GDM, and ZO-Adam and track the corresponding mean-square stability quantities

Reference 13

Resolution: unresolved; no resolver link, observed 2026-07-12T20:06:39.488359Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 20fb8caa-a026-4dca-a067-72315341244b · outbound

This paper cites Appendix D.3).

Zeroth-Order Optimization at the Edge of Stability Appendix D.3)

Reference 14

Resolution: malformed identifier; no resolver link, observed 2026-07-12T20:06:39.488359Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 28de6383-3a18-423e-814d-018e357eaf86 · outbound

This paper cites an unresolved cited work.

Zeroth-Order Optimization at the Edge of Stability Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-12T20:06:39.488359Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d22d7e19-3c7f-47da-b337-c746d9bf0847 · outbound

This paper cites an unresolved cited work.

Zeroth-Order Optimization at the Edge of Stability Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-12T20:06:39.488359Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.